Simplify; express your answer in exponential form. Assume $p\neq 0, y\neq 0$. $\dfrac{{(p^{4})^{-3}}}{{(p^{2}y^{-5})^{-5}}}$
Solution: To start, try working on the numerator and the denominator independently. In the numerator, we have ${p^{4}}$ to the exponent ${-3}$ . Now ${4 \times -3 = -12}$ , so ${(p^{4})^{-3} = p^{-12}}$ In the denominator, we can use the distributive property of exponents. ${(p^{2}y^{-5})^{-5} = (p^{2})^{-5}(y^{-5})^{-5}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(p^{4})^{-3}}}{{(p^{2}y^{-5})^{-5}}} = \dfrac{{p^{-12}}}{{p^{-10}y^{25}}}$ Break up the equation by variable and simplify. $\dfrac{{p^{-12}}}{{p^{-10}y^{25}}} = \dfrac{{p^{-12}}}{{p^{-10}}} \cdot \dfrac{{1}}{{y^{25}}} = p^{{-12} - {(-10)}} \cdot y^{- {25}} = p^{-2}y^{-25}$.